(a) Write a detailed mechanism for the isomerization of -D-fructofuranose from the hydrolysis of sucrose into an...

(a) Write a detailed mechanism for the isomerization of β-D-fructofuranose from the hydrolysis of sucrose into an equilibrium mixture of the β-pyranose and β-furanose forms. 

(b) Although fructose usually appears as a furanose when it is part of a polysaccharide, in the pure crystalline form, fructose adopts a β-pyranose structure. Draw β-D-fructopyranose in its most stable conformation. In water at 20°C, the equilibrium mixture contains about 68% β-dpyranose and 32% β-D-furanose. 

(c) What is the free-energy difference between the pyranose and furanose forms at this temperature? 

(d) Pure β-D-fructopyranose has [α]_D^20°C = -132. The equilibrium pyranose – furanose mixture has [α]_D^20°C = -92. Calculate [α]_D^20°C for pure β-dfructofuranose.